16/05, 2024

Definitions

  • \(\text{L}\) represents the set of Landuses.
  • \(\text{C}\) represents the set of Cells.
  • \(\text{S}\) represents Richness.
  • \(\text{PD}\) represents PhyloDiversity.
  • \(\text{R}\) represents Rarity.
  • \(\text{CC}\) represents CanChange.
  • \(\text{SCB}\) represents SpatialContiguityBonus.
  • \(\text{EN}\) represents Existingnature.

Biodivesity

\[\color{Red}{\text{Biodiversity} = \sum_{l}^L \sum_{c}^C \text{LD}_{l,c} \times \frac{\text{S}_{l,c} + \text{PD}_{l,c} + \text{R}_{l,c}}{3} \times \text{CC}_{c}}\]

Contiguity to new nature

\[ \color{Blue}{\text{Contiguity to new} = \text{SCB} \times \sum_{(i,j)}^E \sum_{l}^L \sum_{c}^C \text{LD}_{l,i} \times \text{LD}_{l,j} \times \text{CC}_{i} \times \text{CC}_{j} } \]

Contiguity to existing nature

\[ \color{Green}{\text{Contiguity to existing} = \text{SCB} \times \sum_{(i,j)}^E \sum_{l}^L \sum_{c}^C \text{LD}_{l,i} \times \text{EN}_{l,j} \times \text{CC}_{i}} \]

Optimization function

\[ \text{maximize CI} = \color{Red}{\text{Biodiversity}} + \color{Purple}{\text{SCB}} \times \left( \color{Blue}{\text{Cont}_n} + \color{Green}{\text{Cont}_{ex}} \right) \]

  • Spatial Contiguity Bonus (SCB) is a dial

Example Landuse (Global contribution)

\[ \text{maximize CI} = \color{Red}{\text{Biodiversity}} + \color{Purple}{\text{SCB}} \times \left( \color{Blue}{\text{Cont}_n} \right) \]

Local contribution

Before after